$On classifying the non-Tits $P$-critical posets$

On classifying the non-Tits $P$-critical posets

In 2005, the authors described all introduced by them $P$-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by u...

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Date:	2022
Main Authors:	Bondarenko, V. M., Styopochkina, M. V.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2022
Subjects:	Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form $0$-balanced subposet $P$-critical poset Tits $P$-critical poset 15B33 15A30
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912
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Journal Title:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-1912
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-19122022-04-15T07:11:32Z On classifying the non-Tits $P$-critical posets Bondarenko, V. M. Styopochkina, M. V. Hasse diagram, Kleiner's poset, minimax equivalence, quadratic Tits form, $0$-balanced subposet, $P$-critical poset, Tits $P$-critical poset 15B33, 15A30 In 2005, the authors described all introduced by them $P$-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits $P$-critical posets as a special case of the $P$-critical posets. In this paper we classify all the non-Tits $P$-critical posets without complex calculations and without using the list of all $P$-critical ones. Lugansk National Taras Shevchenko University 2022-03-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912 10.12958/adm1912 Algebra and Discrete Mathematics; Vol 32, No 2 (2021) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912/pdf Copyright (c) 2022 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2022-04-15T07:11:32Z
collection	OJS
language	English
topic	Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form $0$-balanced subposet $P$-critical poset Tits $P$-critical poset 15B33 15A30
spellingShingle	Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form $0$-balanced subposet $P$-critical poset Tits $P$-critical poset 15B33 15A30 Bondarenko, V. M. Styopochkina, M. V. On classifying the non-Tits $P$-critical posets
topic_facet	Hasse diagram Kleiner's poset minimax equivalence quadratic Tits form $0$-balanced subposet $P$-critical poset Tits $P$-critical poset 15B33 15A30
format	Article
author	Bondarenko, V. M. Styopochkina, M. V.
author_facet	Bondarenko, V. M. Styopochkina, M. V.
author_sort	Bondarenko, V. M.
title	On classifying the non-Tits $P$-critical posets
title_short	On classifying the non-Tits $P$-critical posets
title_full	On classifying the non-Tits $P$-critical posets
title_fullStr	On classifying the non-Tits $P$-critical posets
title_full_unstemmed	On classifying the non-Tits $P$-critical posets
title_sort	on classifying the non-tits $p$-critical posets
description	In 2005, the authors described all introduced by them $P$-critical posets (minimal finite posets with the quadratic Tits form not being positive); up to isomorphism, their number is 132 (75 if duality is considered). Later (in 2014) A. Polak and D. Simson offered an alternative way of proving by using computer algebra tools. In doing this, they defined and described the Tits $P$-critical posets as a special case of the $P$-critical posets. In this paper we classify all the non-Tits $P$-critical posets without complex calculations and without using the list of all $P$-critical ones.
publisher	Lugansk National Taras Shevchenko University
publishDate	2022
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1912
work_keys_str_mv	AT bondarenkovm onclassifyingthenontitspcriticalposets AT styopochkinamv onclassifyingthenontitspcriticalposets
first_indexed	2025-07-17T10:30:09Z
last_indexed	2025-07-17T10:30:09Z
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On classifying the non-Tits \(P\)-critical posets

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